Problem: $z=-19+3.14i$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=-19$ and $\text{Im}(z)=3.14i$ (Choice B) B $\text{Re}(z)=3.14i$ and $\text{Im}(z)=-19$ (Choice C) C $\text{Re}(z)=3.14$ and $\text{Im}(z)=-19$ (Choice D) D $\text{Re}(z)=-19$ and $\text{Im}(z)=3.14$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={-19}+{3.14}i$ is of the form ${a}+{b}i$, where ${a}={-19}$ and ${b}={3.14}$. Therefore: $\text{Re}(z)={a}={-19}$. $\text{Im}(z)={b}={3.14}$. Summary $\text{Re}(z)={-19}$ and $\text{Im}(z)={3.14}$.